Interval-Based Timing Constraints Their Satisfactions and Applications

In real systems, an error range (±Δ) is often given to a time stamp (t) for an observed event. Such practice implicitly states that the event happens anytime in the interval [t-Δ1, t+Δ2]. Hence, constraints based on intervals are more realistic. However, when a constraint is extended from a point to an interval, its satisfaction is not a simple Boolean value; instead, a probability is associated with the constraint. We study the satisfaction probability of interval-based timing constraints when event occurrence is non-uniformly distributed in a given time interval. An algorithm is developed to derive implicit constraints from a set of given interval-based constraints. Our study shows that there are bounds for certain constraint configurations. These analytical results are further applied in two application domains in which constraints are based on single and multiple event models, respectively.